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Re: The Moduli 3-Stack of the C-Field

Re: The Moduli 3-Stack of the C-Field

Since that was a rather boring comment, when you write

This is the correct starting point for any actual quantization of the system (as an effective low-energy gravitational higher gauge theory, as it were, but conceivably of relevance also to the full M-theory),

Re: The Moduli 3-Stack of the C-Field

Since that was a rather boring comment,

Much of the process of finalizing an article is boring, unfortunately. But since it has to be done, I am grateful to you for bothering to look for typos! We fixed a bunch more now. Many probably still remain for the moment.

is this the point at which the hard-nosed string theorist takes note?

It’s a step in the right direction, I would think. Your question made me add a sentence to that “essay”.

More could be said here. Let me tell you what I am currently intrigued by:

there have been, roughly three major attempts for formalizing, mathematically, what higher supergravity is all about. I am thinking of

the terminology is still different, there the Stiefel-Whitney classes are called Wu classes.
(A pdf-witness of this is page 3 of Byun: On vanishing of characteristic numbers in Poincaré complexes (pdf))

Anyway, as I tried to recall above, what matters for the discussion of quadratic refinement of the intersection pairing are mod2mod \, 2 Wu classes as on page 229 of your book with Milnor.

I understood – and still understand – your question as asking whther I can see a role also for other modpmod \,p-Wu classes in the present discussion.

To which my reply still is: an evident naive guess is that they might be relevant in refinements of higher powered intersection pairings. Unfortunately, I still don’t know, but I’ll try to think about it.